Q. How do I check the assumptions for a linear regression model?
Answer
Although numeric tests exist for these assumptions, typically it is easiest to evaluate them graphically.

Independence: Are the error terms independent? Assuming your data was collected through a “well designed experiment or a simple random sampling scheme with one observation per subject”, this assumption is met.

Constant variance: Is the variance of the error terms constant? In other words, does the size of the predicted value affect the variance? You can use the residuals vs. fitted plot to check this assumption. If there is any kind of pattern (i.e. fanning effect) in the plot, this assumption might not be met.

Normality: Are the error terms are normally distributed? Evaluate this assumption by checking a QQ plot. If the points on the QQ plot fall near the line, this assumption is met.

Linearity: Is a linear model a good fit for this data? If the trendline in the residuals vs. fitted plot is horizontal, this assumption is met.

Unusual Observations: Do you have high leverage points (extreme in X) or outliers (extreme in Y)? For outliers, consider if points fall within three standard deviations of the mean. For high leverage points, consider the trendline in the scale location plot. It will be roughly horizontal if there are no high leverage points.